Math Problem Statement

  1. Water flows through a 100 mm diameter orifice. The depth of water above the orifice center is 9 m. What is the discharge in m/s if the tank is going downward with an acceleration equal to one - half the acceleration due to gravity? Assume Cr = 0.64 and Cv = 0.98.
  2. A cylindrical water tank 1.2 m diameter, has an orifice 2.5 m above the level ground. At a certain instant, it was observed that a jet gushing through the orifice strikes the ground 6 m from the side of the tank. After a certain time has elapsed, the jet is observed to strike the ground 3.6 m from the same retence point. Neglecting alr resistance and If Cv = 0.97, find how much water has been discharged through the same orifice during the two-given observation.
  3. A canal lock is 6 m wide by 24 m long. The time to empty the lock is 5 minutes. Determine thelarea of two orifice in the lock if the initial head on the orifice is 5.50 m and assuming C = 0.60
  4. A 3 m diameter vertical cylindrical tank has a 10 - cm diameter orifice at its vertical side. The tank is filled with water such that the head on the oritice is 1 m. Neglecting velocity of approach, determine the interval of time for the velocity of the jet to change from 10 m/s to 7 m/s. Assume Ce = 0.61 and Cr = 0.98,
  5. A jet is issued from the side of a tank under a constant. The side of the tank has an inclination of 1H:1V. The total depth of water in the tank is 8 m and the orifice is located 2.5 m above the bottom of the tank. Neglecting air resistance and assuming Cv = 0.82, determine the following: A. The maximum height to which the jet will rise above the orifice, in meters. B. The point "X" the jet will strike a horizontal plane 1.30 m below the bottom of the tank, in meters. C. The time it takes for the jet to strike the plane in seconds.

Solution

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Math Problem Analysis

Mathematical Concepts

Fluid Mechanics
Bernoulli's Equation
Torricelli's Law
Projectile Motion

Formulas

Torricelli's law
Bernoulli's equation

Theorems

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Suitable Grade Level

Undergraduate Level

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